In section , we derive a general BRST and anti-BRST invariant
formulation of the \({\mathcal {N}=0}\)  theory and show how the action used
in [1]} may be obtained as a special case of
this general formulation. In
section , we reconsider in greater detail the convolutional
relation studied in [1]}. In contrast to [1]}, we do
not constrain the gravitational field ansätze using the equations of
motion, because as explained above terms may be absorbed into the source
term, making such conditions arbitrary. We rely solely on the BRST and
anti-BRST transformations to constrain the ansätze. We derive the
double copy relation for the sources in section REF .
Our results are broadly in agreement with those of [1]}. We
highlight the fact that there is freedom in choosing the coefficients in
the ansätze. In particular, the choice made by [1]} leads to
a breakdown of the double copy relation when the Yang-Mills gauge-fixing
parameter \(\xi =1\) . This behaviour is an artefact of the choice made in
[1]} and there is another choice for which this behaviour is
not observed and moreover the equation for the gravitational source term
is simpler.
